burgers_dg.cc
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#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "harten.h"
#include "burgers.icc"
#include "burgers_flux_godunov.icc"
#include "runge_kutta_ssp.icc"
int main(int argc, char**argv) {
environment rheolef (argc, argv);
geo omega (argv[1]);
space Xh (omega, argv[2]);
Float cfl = 1;
limiter_option lopt;
size_t nmax = (argc > 3) ? atoi(argv[3]) : numeric_limits<size_t>::max();
Float tf = (argc > 4) ? atof(argv[4]) : 2.5;
size_t p = (argc > 5) ? atoi(argv[5]) : ssp::pmax;
lopt.M = (argc > 6) ? atoi(argv[6]) : u_init().M();
if (nmax == numeric_limits<size_t>::max()) {
nmax = (size_t)floor(1+tf/(cfl*omega.hmin()));
}
Float delta_t = tf/nmax;
integrate_option iopt;
iopt.invert = true;
trial u (Xh); test v (Xh);
form inv_m = integrate (u*v, iopt);
vector<field> uh(p+1, field(Xh,0));
uh[0] = interpolate (Xh, u_init());
branch even("t","u");
dout << catchmark("delta_t") << delta_t << endl
<< even(0,uh[0]);
for (size_t n = 1; n <= nmax; ++n) {
for (size_t i = 1; i <= p; ++i) {
uh[i] = 0;
for (size_t j = 0; j < i; ++j) {
field lh =
- integrate (dot(compose(f,uh[j]),grad_h(v)))
+ integrate ("internal_sides",
compose (phi, normal(), inner(uh[j]), outer(uh[j]))*jump(v))
+ integrate ("boundary",
compose (phi, normal(), uh[j], g(n*delta_t))*v);
uh[i] += ssp::alpha[p][i][j]*uh[j] - delta_t*ssp::beta[p][i][j]*(inv_m*lh);
}
uh[i] = limiter(uh[i], g(n*delta_t)(point(-1)), lopt);
}
uh[0] = uh[p];
dout << even(n*delta_t,uh[0]);
}
}
burgers.icc
The Burgers equation – the f function.
main
int main(int argc, char **argv)
Definition: burgers_dg.cc:32
g
u_exact g
Definition: burgers_diffusion_exact.h:33
u_init
u_exact u_init
Definition: burgers_diffusion_exact.h:32
lh
field lh(Float epsilon, Float t, const test &v)
Definition: burgers_diffusion_operators.icc:25
burgers_flux_godunov.icc
The Burgers equation – the Godonov flux.
Float
see the Float page for the full documentation
branch
see the branch page for the full documentation
field
see the field page for the full documentation
form
see the form page for the full documentation
geo
see the geo page for the full documentation
rheolef::catchmark
see the catchmark page for the full documentation
Definition: catchmark.h:67
rheolef::environment
see the environment page for the full documentation
Definition: environment.h:115
rheolef::integrate_option
see the integrate_option page for the full documentation
Definition: integrate_option.h:125
rheolef::integrate_option::invert
bool invert
Definition: integrate_option.h:168
rheolef::std
Definition: vec_expr_v2.h:402
rheolef::point
point_basic< Float > point
Definition: point.h:164
rheolef::dout
odiststream dout(cout)
see the diststream page for the full documentation
Definition: diststream.h:430
rheolef::field
field_basic< Float > field
see the field page for the full documentation
Definition: field.h:419
space
see the space page for the full documentation
test
see the test page for the full documentation
trial
see the test page for the full documentation
harten.h
The Burgers problem: the Harten exact solution.
mkgeo_ball.n
int n
Definition: mkgeo_ball.sh:150
rheolef
This file is part of Rheolef.
Definition: compiler_eigen.h:37
rheolef::limiter
field_basic< T, M > limiter(const field_basic< T, M > &uh, const T &bar_g_S, const limiter_option &opt)
see the limiter page for the full documentation
Definition: limiter.cc:65
rheolef::dot
rheolef::std enable_if ::type dot const Expr1 expr1, const Expr2 expr2 dot(const Expr1 &expr1, const Expr2 &expr2)
dot(x,y): see the expression page for the full documentation
Definition: vec_expr_v2.h:415
rheolef::grad_h
std::enable_if< details::is_field_convertible< Expr >::value,details::field_expr_v2_nonlinear_terminal_field< typename Expr::scalar_type,typename Expr::memory_type,details::differentiate_option::gradient >>::type grad_h(const Expr &expr)
grad_h(uh): see the expression page for the full documentation
Definition: field_expr_terminal.h:949
rheolef::integrate
std::enable_if< details::is_field_expr_v2_nonlinear_arg< Expr >::value &&! is_undeterminated< Result >::value, Result >::type integrate(const geo_basic< T, M > &omega, const Expr &expr, const integrate_option &iopt, Result dummy=Result())
see the integrate page for the full documentation
Definition: integrate.h:202
rheolef::interpolate
field_basic< T, M > interpolate(const space_basic< T, M > &V2h, const field_basic< T, M > &u1h)
see the interpolate page for the full documentation
Definition: interpolate.cc:233
rheolef::compose
details::field_expr_v2_nonlinear_node_nary< typename details::function_traits< Function >::functor_type,typename details::field_expr_v2_nonlinear_terminal_wrapper_traits< Exprs >::type... > ::type compose(const Function &f, const Exprs &... exprs)
see the compose page for the full documentation
Definition: compose.h:246
rheolef::normal
details::field_expr_v2_nonlinear_terminal_function< details::normal_pseudo_function< Float > > normal()
normal: see the expression page for the full documentation
Definition: field_expr_terminal.h:439
ssp::beta
Float beta[][pmax+1][pmax+1]
Definition: runge_kutta_ssp.icc:40
ssp::alpha
Float alpha[][pmax+1][pmax+1]
Definition: runge_kutta_ssp.icc:28
ssp::pmax
constexpr size_t pmax
Definition: runge_kutta_ssp.icc:26
rheolef.h
rheolef - reference manual
runge_kutta_ssp.icc
The strong stability preserving Runge-Kutta scheme – coefficients.
f
Definition: cavity_dg.h:29
p
Definition: sphere.icc:25
phi
Definition: phi.h:25
rheolef::limiter_option
see the limiter page for the full documentation
Definition: limiter.h:72
rheolef::limiter_option::M
Float M
Definition: limiter.h:75
u_exact::M
Float M() const
Definition: burgers_diffusion_exact.h:29
u
Definition: leveque.h:25
u
Float u(const point &x)
Definition: transmission_error.cc:26